Can a New Law of Physics Explain a Black Hole Paradox?

In this video, Leonard Susskind describes how black holes challenge traditional thermodynamics by continuing to evolve long after reaching thermal equilibrium, a paradox that led him to propose a new “second law of quantum complexity.” He explains that while entropy maxes out almost immediately, a black hole’s interior spacetime keeps growing, and the key insight is that this growth directly measures the quantum computational complexity of its state. Unlike classical bits, quantum qubits can be globally entangled, allowing complexity to increase far beyond what entropy captures—creating a kind of “life after heat death.” Borrowing the concept of quantum circuit complexity from computer science, Susskind and collaborators conjectured that complexity, like entropy, increases on average until it reaches its own maximum. The idea initially met skepticism for equating physical volume with a difficult-to-compute quantity, but later work using cryptographic scrambling and quantum chaos supported the framework. Ultimately, the second law of complexity remains a conjecture most clearly applicable to black holes, with open and potentially major implications for the evolution of the universe as a whole.

• ▶ 0:40 After thermal equilibrium, quantum entanglement keeps evolving, inspiring a proposed “second law of quantum complexity” in analogy with thermodynamics.
• ▶ 1:35 Susskind found a black hole’s interior spacetime can grow forever, creating a paradox since thermodynamic laws demand a final equilibrium or heat death.
• ▶ 2:07 Susskind and collaborators sought to resolve the paradox, leading to an unexpected explanation tied to complexity.
• ▶ 2:18 Susskind contrasts his practical “auto mechanic” mindset with Feynman’s visual, mathematical approach: “What works is what's practical, but sometimes you need some mathematics.”
• ▶ 2:40 He highlights the puzzling feature of black holes he first encountered—unrelated to complexity—introduced through Penrose diagrams, “a kind of map of the whole universe, including a black hole,” with time going upward.
• ▶ 3:02 The key anomaly: the black hole interior’s geometry shrank to a smallest size, then bounced and expanded—something Susskind didn’t understand and initially gave up on, with experts only vaguely calling it “just the volume of the black hole.”
• ▶ 3:58 Entropy is a statistical claim: systems naturally move toward greater disorder, defining the arrow of time.
• ▶ 4:07 Susskind rejected entropy as the answer because a black hole reaches maximum entropy almost immediately, while its dynamics continue for a very long time.
• ▶ 4:52 Thermodynamic equilibrium is not the end of the story; closed quantum systems need a separate notion of complexity equilibrium, which continues to evolve long after thermal equilibrium.
• ▶ 5:13 Susskind and collaborators applied theoretical computer science to black holes, suspecting complexity underlies their continued growth past thermal equilibrium.
• ▶ 5:41 Because the number of quantum states grows exponentially with qubits, a quantum system takes enormously long to explore state space—much longer than the time to reach thermal equilibrium.
• ▶ 6:16 The key breakthrough: the size of a black hole's interior directly measures the computational complexity of its quantum state, sparking deep interest in complexity.
• ▶ 6:36 Classical systems can be described as a collection of independent, individually specified bits.
• ▶ 6:48 Quantum systems cannot be described bit-by-bit because qubits can be globally entangled.
• ▶ 7:00 Local qubits may contain no information, yet the global system can hold a highly non-trivial quantum state.
• ▶ 7:07 Entanglement is the key reason quantum complexity can grow far beyond what classical systems can encode.
• ▶ 7:14 Susskind and Brown propose that a black hole's interior can keep evolving after classical entropy maxes out, driven by the ever-increasing complexity of its quantum state, yielding "life after heat death" at ▶ 7:28.
• ▶ 7:33 They borrow "circuit complexity" from computer science, transforming it into quantum circuit complexity as the "unlikely mathematical language" for a new theory of black hole evolution [7:44–7:52].
• ▶ 7:57 A computer scientist recalls skepticism about the idea, noting that equating physical volume with quantum circuit complexity—something "manifestly hard to compute"—felt "really provocative" yet hard to believe [8:24–8:44].
• ▶ 8:52 Researchers tested Susskind and Brown's theory using tools from modern cryptography, comparing quantum states to a quantum analog of a block cipher.
• ▶ 9:20 The link between cryptographic scrambling and chaotic mixing of qubits in a quantum system ended up supporting Susskind's approach.
• ▶ 9:47 Unexpectedly, the work justified Susskind's conjectures, suggesting his framework was the only sensible way to resolve the paradox.
• ▶ 10:24 Susskind and collaborators proposed a new fundamental law: a "second law of complexity," stating that complexity—like entropy—increases on average until it maxes out.
• ▶ 10:52 This is a conjecture, not a proven law; it most clearly applies to black holes, while its application to the whole universe remains unclear.
• ▶ 11:19 The idea relies on fully quantum circuit complexity, shifting to a quantum description from within the quantum world—with potentially major, unexplored implications for the universe's evolution, including complexity's own analog of heat death.

• ▶ 0:01 The Second Law and the Black-Hole Interior Growth Paradox (0:01 - 2:18) - Introduces the second law of quantum complexity and the paradox of expanding black-hole interiors.
• ▶ 2:18 Susskind, Feynman, and Penrose Diagrams (2:18 - 3:31) - Recalls Feynman’s visual style and uses Penrose diagrams to frame the black-hole problem.
• ▶ 3:31 Entropy and the Need for Complexity Equilibrium (3:31 - 5:04) - Moves from entropy to complexity equilibrium as the missing concept for closed quantum systems.
• ▶ 5:04 Complexity and Black Hole Interiors (5:04 - 6:36) - Defines complex systems and applies their many interacting parts to black-hole interiors.
• ▶ 6:36 Entanglement and Quantum Complexity (6:36 - 7:14) - Shifts from classical bits to quantum entanglement as the basis for complexity.
• ▶ 7:14 Circuit Complexity and "Life After Heat Death" (7:14 - 8:48) - Susskind and Brown connect quantum circuit complexity to evolution beyond heat death.
• ▶ 8:48 Testing the Theory with Cryptography (8:48 - 10:11) - Cryptographic experiments probe the predicted behavior of quantum circuit complexity.
• ▶ 10:11 The Second Law, Scope, and Cosmic Implications (10:11 - 12:48) - Explains the remarkable second law, its current black-hole scope, and its broader universe and recurrence implications.